I quail hunted for years in Georgia with my 20 gauge GHE skeet gun and the single trigger balked only one time not firing the second barrel. Bobby

I have owned and shot many, many Reproductions and have only had two with doubling problems and a simple cleaning solved the problem on both of them.

Repro
 

I have had doubling issue on two guns, one mine and one belongs to a friend and both were new or like new condition and a good cleaning fixed both.

I own two 12-gauge Parkers with the later version of the factory single trigger and they both work well in R-L and L-R firing sequence. I'm kind of a "trigger toucher" and have to remember to use a little more pressure on that second barrel otherwise its hammer won’t release with my normal light touch. Both guns require about 1.5 - 2 pounds more pull (per my trigger pull gauge) on that second shot no matter which barrel is fired first, which is good. I never had a double fire when shooting a variety of light to heavy loads, or a FTF the second barrel with that little heavier pull. One of the single trigger Parkers is pretty new to me with about 200 shots fired; and the other one has been with me about 3 years now with almost 2000 rounds fired over that period.